Question

Twenty caravans are travelling across the desert on the day apart . The first caravan reached the oasis and the camel drank half of the water in the pool. On the second day the second caravan reached the oasis and the camel drank one third of the water that was left . On the third day the camel in the caravan drank one quater of the water that was left. On the first day pool contained $1050m^3$ of water . How much water was left after the twenty caravan passed through

Answer 1

The first caravan left half of the total water.
So, remaining water after first caravan $=1-\frac{1}{2}=\frac{1}{2}$.....(i)

Second caranan water consumed $=\frac{1}{3}$ of $\frac{1}{2}$ of total water (left by first)
$=\frac{1}{6}$ total water
So, remaining water left after second caravan $=\frac{1}{2}-\frac{1}{6}$
$=\frac{3-1}{6}$
$=\frac{2}{6}$
$=\frac{1}{3}$....(ii)
Third caravan water consumed$=\frac{1}{4}\times \frac{1}{3}$
$=\frac{1}{12}$
So, remaining water left after third caravan$=\frac{1}{3}-\frac{1}{12}$
$=\frac{4-1}{12}$
$=\frac{3}{12}$
$=\frac{1}{4}$.......(iii)

In general, remaining water left after $n^{th}$ caravan $=\frac{1}{n+1}$
Substitute $n=20$ to get remaining water left after ${20}^{th}$ caravan=$\frac{1}{20+1}=\frac{1}{21}$ of initial water.
Thus, the remaining water left after ${20}^{th}$ caravan $=\frac{1}{21}\times 1050$
$=50m^3$